The problem asks which logarithmic equation is equivalent to $243 = 3^x$. Let's analyze:

Step-by-Step Solution:

1. The given equation is $243 = 3^x$.
2. Taking the base-3 logarithm of both sides: $\log_3 243 = \log_3 (3^x).$
3. By the logarithmic rule, $\log_b (a^c) = c \cdot \log_b a$, we simplify: $\log_3 243 = x.$
4. Therefore, the equivalent equation is: $\log_3 243 = x.$

Correct Answer:

The correct option is D. $\log_3 243 = x$.

Would you like a deeper explanation or examples? Here are 5 related questions for practice:

1. Solve $81 = 3^y$ and find its equivalent logarithmic form.
2. Rewrite $2^x = 8$ using logarithms.
3. Simplify $\log_5 125$.
4. If $\log_b x = y$, explain what $x = b^y$ means.
5. Convert $\log_{10} 1000 = 3$ into exponential form.

Tip: Remember, $\log_b a = x$ means $b^x = a$. Use this to translate between logarithmic and exponential forms!